Module Six Closing Discussion Board

1. Module Six Closing
Discussion Board

2. Explanation and Example of Independent Events
Independent events are events that have no impact on each other, this
means that the probability of one event does not impact the
probability of the other independent event. An example of this would
be rolling a pair of dice, and then flipping a coin. Those two events do
not impact each other in any way.

3. Explanation and Example of Mutually
Exclusive Events
Mutually exclusive events are a set of events that cannot happen at the
same time together. An example of this would be a fork in the road
where you can either turn left, or right. You cannot go both ways at the
same time, therefore making the events mutually exclusive.

4. Explanation of Conditional Probability
Conditional Probability is the probability of an event occuring that has
some relationship with another event.
Example: In a group of 100 sports car buyers, 40 bought alarm systems,
30 purchased bucket seats, and 20 purchased an alarm system and
bucket seats. If a car buyer chosen at random bought an alarm system,
what is the probability they also bought bucket seats?
Formula: P(B|A) = P(A∩B) / P(A)
Answer: P(B|A) = P(A∩B) / P(A) = 0.2 / 0.4 = 0.5.

5. Explanation of the Addition Rule of
Probability
Addition Rule Part One: When two events are mutually exclusive, the probability that a A or B will
occur is the sum of the probability of each event.
Example: A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?
Formula: P(A or B) = P(A) + P(B)
Answer: 2/6 or 1/3
Addition Rule Part Two: When two events, A and B, are non-mutually exclusive, the probability that
A or B will occur is:P(A or B) = P(A) + P(B) - P(A and B)
In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made
an A grade. If a student is chosen at random from the class, what is the probability of choosing a
girl or an A student?
Answer: 17/30

6. Explanation of the Multiplication Rule of
Probability
This rule states that if the events come from the same sample space
that the probability of them both occuring is the probability of A times
the probability of B given that A occurs. P(A ∩ B) = P(A) P(B|A)
Example: Whats the probaility of pulling a king and then an ace out of a
standard deck of cards without replacement.
4/52 x 4/51 = 4/663

7. An Event Where the Theoretical Probability is
One Out of Three
If you were to role a die with 3 sides, the theoretical probability that
you would land on the number 3 is 1/3.

8. Marginal Probability Question
Fill in the marginal probabilities.
Answer:

9. Joint Probability Question
What is the probability that someone got the flu shot and did not get
the flu?
Answer: P(A and B) = .47

10. Conditional Probability Question
What is the probability that someone got the flu given that they did not
get the flu shot?
Answer: .41/.46 or 89%